Continental Airlines and Western Airlines yesterday announced the beginning of exploratory discussions aimed at a merger.

Such a merger would have to be approved by the boards of directors and stockholders of both companies and, more importantly, by the Civil Aeronautics Board and the president of the United States, the president's approval would be needed because international routes would be involved.

It is not known how the CAB would react to a petition for approval of a Continental-Western merger. A CAB official would say only that the agency would look at it "very carefully." But approval would reverse a long-standing board policy of refusing to approve mergers of traditionally profitable airlines.

Although many of the board's longstanding policies have been abandoned in the recent past, it is felt that the current board, with a clearly procompetitive bent, would approve a merger of two healthy competitors only if it could be convinced the combination would benefit competition and the traveling public.

Continental and Western are two of the smaller of the nation's major regulated airlines. They have similar characteristics: both are headquartered in Los Angeles and both operate mainly in the West with similar air craft.

Both also have applicants pending at the board for new route authority on each other's routes and both are vying for some of the same routes that neither now have. The two carriers' officials say they now compete directly on three routes: Los Angeles-Honolulu, Los Angeles-Phoenix, and San Diego-Denver.

Both carriers have been consisently profitable. Last year, Continental reported the highest annual profit, in the company's history, $25.6 million on revenues of $657 million. Western, which has reported profits every year but one is nearly 30 years, had profits of $14.4 million on revenues of $691 million.

Company officials said yesterday the exploratory discussions have followed a preliminary joint study of a possible merger by the staffs now, they point out, discussions at the executive level will be held.

Continental tried to merge with Western once before, but Western decided to seek a merger with American Airlines instead. The proposed merger was turned down by the CAB in 1972.

Meanwhile, at the CAB meeting yesterday, the board voted tentatively to give five airlines, including two that would be given their first interestate routes, the authority to begin low-fare service in and out of Chicago's Midway Airport serving six midwestern cities.

Scheduled to get the new interstate operatisng authority are Midway Airlines, a new company headed by Irving Tague, former president of Hughes Air West, and Midway (Southwest) Airway, subsidiary of Southwest Airlines, a successful Texas air carrier.

The two told the board in applications filed in late 1976 they would provide nonstop air service at fares up to 50 percent below existing coach fares between Midway and Minneapolis/St. Paul, Kansas City, St. Louis, Detroit, Cleveland and Pittsburgh.

Three other airlines - Delta Air Lines, Northern Central Airlines, and Northwest Airlines - also will get Midway operating rights.

The tentative vote was 3 to 1, with Richard O'Melia the dissenter; he felt the two new airlines needed some lead time to get started before the other carriers began their Midway service.

The board also instituted a new proceeding, called Midway II, which will look at the need for more low-fare service to Midway from 17 additional cities, including Washington.